Simple.
Divide the guide number by the distance and you get the aperture you need.
So if a flash has a guide number of 120 feet at ISO 100 (they are usually quoted at ISO 100) and you want to use it eight feet away from the subject, the aperture you need is 120/8 = 15. Nearest real aperture setting of f16 is close enough.
To test the theory that if you double the distance, the light level is reduced to 1/4, lets try it at 16 feet.
120/16 = 7.5. close enough to f8 which is two stops away from f16 and therefore, 1/4 of the light.
Steve.